I'm considering:
\[(1+x)^{10} = \left(\begin{matrix}10 \\ 0\end{matrix}\right) +\left(\begin{matrix}10 \\ 1\end{matrix}\right)x + \left(\begin{matrix}10 \\ 2\end{matrix}\right)x^2 + \left(\begin{matrix}10 \\ 3\end{matrix}\right)x^3 + ... + x^{10} \]
But i have no idea where to go from here.
If i look at the RHS, then i came up with something....?: \[2^9 ( 2^{10} + 1) \rightarrow 2^{n-1} (2^{n} +1) \]
But i'm not how to get there :/
I also noticed on the LHS, the things are all even. Idk -.-

when x=3, ive already worked the numerator to 2^(10) [2^(10)+1]
right?

butterflydreamer

2 years ago

yes

amistre64

2 years ago

then it is proofed

butterflydreamer

2 years ago

hmm okay then. Thank you!
It's just that for the prev. questions i've been working on, i've had to use a range of differentiation/integration and substitution methods so i thought this question would've involved similar steps but thanks again!
Your method was way simpler.